We are working on data with no fieldmap and we would like to code the guidelines of (Zhan et al. 2015, http://dx.doi.org/10.3389/fnagi.2015.00048) with eddy which has shown to work perfectly with phase encoded fieldmaps for topup.

In particular, we are working on ADNI dataset. Usually, we need fieldmap to correct for EPI distortion. However, there is no fieldmap data for ADNI2. Since T1 is less likely to be affected by EPI distortion, we would like to perform these operations :

1) Use eddy to correct for HM and EC

2) Perform a non linear registration of the b=0 your DWI data to T1 for the Susceptibility Distorsion step

3) Combine 1) and 2) in order to generate a single deformation and minimise the number of interpolations for the final preprocessed DWI

To combine 1) and 2), we would need to convert outputs of eddy for a flirt format.

I think you are weighing the different sources of error wrong here. By limiting the eddy transform to a linear transform I think you will introduce larger errors than you would from two interpolations. If you use spline interpolation the degradation is very much at all. You can do a little experiment where you rotate/transform an image N times until it is back in its original position and see how big the difference is compared to the original. If you do that you will see that one trilinear interpolation (the way we used to do things) corresponds to ~spline interpolations. So two really isn’t the end of the world. In contrast the eddy current correction you get from just the linear part is often (depending on acquisition details) visibly poorer than if you use a quadratic model.

Another option for combining them is to take the deformation field you get from your b0-T1 registration, discard the components that are not in the PE-direction (these are anyway wrong), rescale it to Hz and feed it into the --field parameter in eddy.

Jesper

Alexandre

Le mar. 28 août 2018 à 17:10, Jesper Andersson <[log in to unmask]> a écrit :

Dear Alexandre,

maybe if you explain in a little more detail what you want to do I can give better advice. Why do you want to create your own flirt matrices instead of using the resampling that eddy gives you?

Jesper

On 28 Aug 2018, at 15:29, Alexandre Routier <[log in to unmask]> wrote:

Dear Jesper,

Thanks for your explanations. I am not a specialist in MRI so I am not sure to understand how to interpret correctly the columns 7 to 9 explaining the linear EC-terms or to combine the rigid transformation with the off-resonance field.

In my first message, I separated the "affine" from the rigid part but in practice, one single transformation would suit me perfectly.

Best,

Alexandre

Le mar. 28 août 2018 à 14:43, Jesper Andersson <[log in to unmask]> a écrit :

Dear Alexandre,

it is really a little bit of a misunderstanding that eddy currents causes distortions that correspond to an affine transform. The notion, I think, comes from the seminal paper by Peter Jezzard. In there he looks specifically at the 2D case and models the distortions as i) A zoom in the PE-direction, ii) A shear in the PE-by-FE-direction and iii) A translation. This model is based on an assumption that the EC-induced field is a superposition of linear gradients in the x-, y- and z-directions (the latter becoming a constant in the 2D case). Hence the EC distortions only correspond to a subset of a 2D affine transform, and methods that attempt to estimate all parameters of an affine run the risk of overfitting and hence poorer precision.

In 3D, with the same assumptions, the distortions become i) A zoom in the PE-direction, ii) A shear in the PE-by-FE-direction and iii) A shear in the PE-by-slice-direction. Again, well short of an affine transform. Furthermore, the assumption that any field induced by eddy currents is a superposition of linear gradients is only a first approximation and not really valid for the scanners I have worked on data from.

For this reason, and also because of how the effect of the EC-induced fields interact with the susceptibility induced field, we don’t use an “affine” transform anywhere in eddy. Instead we combine an off-resonance field with a rigid-body transform. For the linear EC-terms there is a very simple relationship between the numbers in the .eddy_parameters file. The numbers in columns 7-9 give the gradients (in Hz/mm) in the x-, y- and z-directions. I think the easiest for you is to just combine your rigid-body transform (which it sounds like you have already figured out how to generate) with that field.

Jesper


> On 27 Aug 2018, at 12:38, Alexandre Routier <[log in to unmask]> wrote:
>
> Hi,
>
> Do you any idea for my problem?
>
> For question 1), the content of the matrices I give solved my issue and seems to work perfectly.
>
> But for question 2), I have no clue on how to write the affine transformation based on the information I read.
>
> Best,
> Alexandre
>
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